Principles and psychophysics of Active Inference

Laurent Perrinet, ChloƩ Pasturel and Anna Montagnini

Probabilities and Optimal Inference to Understand the Brain


http://invibe.net/LaurentPerrinet/Presentations/2018-04-05_BCP_talk

Principles and psychophysics of Active Inference

Laurent Perrinet, ChloƩ Pasturel and Anna Montagnini

Probabilities and Optimal Inference to Understand the Brain

Outline

  1. A dynamic probabilistic bias in visual motion direction

  2. Raw psychophysical results
  3. The Bayesian Changepoint Detector
  4. Results using the BCP

A dynamic probabilistic bias in visual motion direction

A dynamic probabilistic bias in visual motion direction

A dynamic probabilistic bias in visual motion direction

A dynamic probabilistic bias in visual motion direction

A dynamic probabilistic bias in visual motion direction

Outline

  1. A dynamic probabilistic bias in visual motion direction
  2. Raw psychophysical results

  3. The Bayesian Changepoint Detector
  4. Results using the BCP

Raw psychophysical results

Raw psychophysical results

Raw psychophysical results

Raw psychophysical results

Raw psychophysical results

Raw psychophysical results

Outline

  1. A dynamic probabilistic bias in visual motion direction
  2. Raw psychophysical results
  3. The Bayesian Changepoint Detector

  4. Results using the BCP

The Bayesian Changepoint Detector

The Bayesian Changepoint Detector

The Bayesian Changepoint Detector

Bayesian Changepoint Detector

  1. Initialize
    • $P(r_0)= S(r)$ or $P(r_0=0)=1$ and
    • $ν^{(0)}_1 = ν_{prior}$ and $χ^{(0)}_1 = χ_{prior}$
  2. Observe New Datum $x_t$
  3. Evaluate Predictive Probability $Ļ€_{1:t} = P(x |ν^{(r)}_t,χ^{(r)}_t)$
  4. Calculate Growth Probabilities $P(r_t=r_{t-1}+1, x_{1:t}) = P(r_{t-1}, x_{1:t-1}) Ļ€^{(r)}_t (1āˆ’H(r^{(r)}_{t-1}))$
  5. Calculate Changepoint Probabilities $P(r_t=0, x_{1:t})= \sum_{r_{t-1}} P(r_{t-1}, x_{1:t-1}) π^{(r)}_t H(r^{(r)}_{t-1})$
  6. Calculate Evidence $P(x_{1:t}) = \sum_{r_{t-1}} P (r_t, x_{1:t})$
  7. Determine Run Length Distribution $P (r_t | x_{1:t}) = P (r_t, x_{1:t})/P (x_{1:t}) $
  8. Update Sufficient Statistics :
    • $ν^{(0)}_{t+1} = ν_{prior}$, $χ^{(0)}_{t+1} = χ_{prior}$
    • $ν^{(r+1)}_{t+1} = ν^{(r)}_{t} +1$, $χ^{(r+1)}_{t+1} = χ^{(r)}_{t} + u(x_t)$
  9. Perform Prediction $P (x_{t+1} | x_{1:t}) = P (x_{t+1}|x_{1:t} , r_t) P (r_t|x_{1:t})$
  10. go to (2)

The Bayesian Changepoint Detector

The Bayesian Changepoint Detector

Outline

  1. A dynamic probabilistic bias in visual motion direction
  2. Raw psychophysical results
  3. The Bayesian Changepoint Detector
  4. Results using the BCP

Results using the BCP

Results using the BCP

Results using the BCP

Results using the BCP

Results using the BCP

Results using the BCP

Principles and psychophysics of Active Inference

Laurent Perrinet, ChloƩ Pasturel and Anna Montagnini

Probabilities and Optimal Inference to Understand the Brain